User:Iit bpd1962

Paradoxes, God and Logic: All Employed Heuristically Towards Arriving at Truth

Axiom 0: An ([1]) entity is any cognizable notion.

Axiom 1: "I experience" or "I exist" can be viewed as advertising one's physical existence. The material world exists (René Descartes' statement "I think, therefore I exist", [2], which, through personal experience, is a neccessary and sufficient starting minimal axiom for generating a complete Logic system ).

[Reduction, to atomic axioms, is employed as it makes the point about the nature of axioms, viz., that a starting axiom shall be as atomic or non divisible as is possible, until experience itself acts as a halter to further reduction, or, to a contradiction, or, to recursive / self referential staements, shall NOT be allowed. The latter "diss allowance" cannot be over emphasized. Any self referetial arument which includes notions of existence AND notions of existence with energy, must be based on experience, else one is assuming what one wants to prove in the first place. Further, paradoxes result because of allowance to self referential statements. Extreme importance to the use of experience as the ONLY source of Knowledge, is being strongly employed here. Such a notion is completely borrowed from the originator or author of the notion, viz., "All our knowledge is based upon experience", by Swami Vivekananda [3]. Kindly use this link to then click on the left frame content viz., "Introduction", then do the same on "Raja-Yoga" and finally on "Introductory"; direct access to the frame causes some suspicious problems in the act of cut/paste operations.

Axiom 2: Applications of Godel's 1st Incompleteness Theorem, [4] are under scrutiny: The apparent non acknowledgement of the nature of material and platonic paradigms, including, the non addressing of the temporal aspect of nature ( tense logic ) [5], seems to have introduced "incompleteness" in the arguments using Godels Incompleteness Theorem.

Reference taken from ([6])Russell's paradox (also known as Russell's antinomy) is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Frege is contradictory. Consider the set M to be "The set of all sets that do not contain themselves as members". Formally: A is an element of M if and only if A is not an element of A.

Let M = U, let A = {E1, E2,......, \infty}; where the Eith term corresponds to the i_th idea.

Let U = { A | A \not\in A} ...... (1)

Question: Does U contain itself?

If YES, then U by (1) above does not contain itself, meaning, if U then \bar{U}

Implication: U = {Ø}, the null set.

Proof: Transformation, if U then \bar{U}

Means U AND \bar{U} is TRUE \equiv YES

Let U = 1 (1 \in set of Natural Numbers; meaning, U to be a set of all true ideas which is a set that does not contain itself.

[7]AND, OR, ... will be now used.

Using the Boolean operator AND, we get,

U AND \bar{U} = TRUE = 1

\Rightarrow 1 AND 0 = True

But 1 AND 0 = 0

This is possible iff U = {Ø}, is 8 null set

Hence if the paradox itself is considered as a notion, we have just shown the paradox to be a null set, which implies that Russel's paradox itself does not, or cannot, exist.

Now, if YES, U \Rightarrow \bar{U}

OR

if NO, \bar{U} \Rightarrow U

This is possible only iff U = {Ø}.

We used U = 1. Now we use a set of \infty U = God = G; ideas which are an element of U

ConclusionItalic text: God does not exist as an entity "looking down/up at Earth" (i.e the dualistic philosophy is not true) and shall exist when the universe unities as one entity, the Big-Crunch, for want of an expression.

Interpretation: U \Rightarrow \bar{U}

OR

if NO, \bar{U} \Rightarrow U

Can be written as letting U = G

if YES, G \Rightarrow \bar{G}

OR

if NO, \bar{G} \Rightarrow G

\Rightarrow G AND \bar{G} co-exist.

But G AND \bar{G} = 0 by definition

also \bar{G} AND G = 0

De Morgan theorem states if G AND \bar{G} = 0

then negation of G AND \bar{G} = 1

Said otherwise \bar{G} OR G = 1

Therefore we can say, (God exists) OR (God does not exist) is TRUE

Since we can define 1 = TRUE

(but not both (G, \bar{G}) together).

Let infinite knowledge = 1 i.e., = TRUE implies that (either God exists) AND (the material world does not exist) OR (the material world exists) AND (God does not exist.)

Conclusion: The semantics of the notion such as god and the semantics of notions of infinite knowledge called the paradigm of mathematics are identical. It may be paranthetically added that all universe particles (entities) have the attribute of God.

Paradoxes simply cannot "exist". They seem to exist due to incomplete / clever formulations of statements; ie., without recourse to temporal logic while assuming implicitly that time exists (which may not exist). Also, such paradoxes assume Integral Calculus to lead to Truth in this discrete material world, thus, indulging in subtle results which appear as paradoxes. Even Einstein's Twin paradox maybe resolved when the Relativity Theories are indulged in by employing axioms based on experienced physical phenomenon; when applied to reality, that while, time may not exist, frequencies and rates of energy entities do exist. Such energy entities may be (discrete and NOT continuous), or (continuous AND not discrete); however, these entities could have boundary conditions amounting to notions of continuity; that ( Nature is continuous ) OR, but not both together, ( nature is discreate ), depends upon the manner in which that entity is examined; Quantumn mechanics shall be employed and then interpreted, keeping in mind the TRUTH of this non-duality / (simultainity of observing two possibilities is impossible) possibility.

The author is not hesistant in including notions such as infinite knowledge, God and mathematics, since the search for Truth fortunately / unfortunately requires one to boldly venture into supposedly unknown / suspicious paradigms. For a holistic cognition wherein atomic axioms are re-examined and / or, re-stated, kindly visit [9], a page which describes why Time CANNOT exist and Space CANNOT exist, in the form we view it; A fefreshed list of Axioms are mentioned here.

Keywords: Experience, Events, Time, Space, Axiom, Logic, Knowledge, God, Infinity, Discrete, Continous, Integral Calculus, Paradoxes. Retrieved from "http://en.wikipedia.org/wiki/User:Iit_bpd1962" Views